1. Field of the Invention
The present invention pertains to RF signatures of complicated enclosures, and more particularly relates to a system and method to determine a unique Electromagnetic Fingerprint for a complicated enclosure and to remotely interrogate and learn the identity of a complicated enclosure.
2. Background
Ray chaos is a well-defined mathematical concept. It can be defined abstractly in terms of the ‘extreme sensitivity to initial conditions.’ Chaotic systems are deterministic in the sense that there are precise mathematical equations that govern the evolution of the system. However, the solutions to those equations are extremely sensitive to the initial conditions. This makes it very difficult to make long-term predictions about chaotic systems because they are extremely sensitive to initial conditions and noise.
Formally, imagine two solutions (x1(t) and x2(t), where t is time) to the equations that govern the system. Assume that the two solutions arise from slightly different initial conditions. As the system evolves, the trajectories described by those solutions will diverge from each other. The divergence can be quantified by Δx(t)=x1(t)−x2(t)˜eλt. The quantity λ is the Lyapunov exponent of the system (generally, there is more than one). If the largest Lyapunov exponent of the system is positive, then the trajectories will diverge as a function of time, and chaos exists.
This definition can be applied to rays propagating inside complicated enclosures. A mathematical ray starting inside the enclosure from a certain point and going in a specific initial direction will travel straight through free space until it encounters a wall or other obstruction. At that point it undergoes specular scattering (angle of incidence=angle of reflection) and moves off in a new direction to encounter another obstruction, bounce there, and so on. A second ray starting from a slightly different position and pointing in a slightly different initial direction will follow its trajectory in the same manner. The distance between the two rays can be calculated as a function of time, as can the distance between scattering sites of the two rays. If there is ray chaos, these distance measures will increase exponentially in time, at least initially.